{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:04:46Z","timestamp":1776845086124,"version":"3.51.2"},"reference-count":45,"publisher":"Elsevier BV","issue":"3","license":[{"start":{"date-parts":[[2004,7,1]],"date-time":"2004-07-01T00:00:00Z","timestamp":1088640000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2004,7,1]],"date-time":"2004-07-01T00:00:00Z","timestamp":1088640000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["OGP0007353"],"award-info":[{"award-number":["OGP0007353"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science and Technology","doi-asserted-by":"publisher","award":["14005245"],"award-info":[{"award-number":["14005245"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science and Technology","doi-asserted-by":"publisher","award":["14540051"],"award-info":[{"award-number":["14540051"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Mathematics and Computation"],"published-print":{"date-parts":[[2004,7]]},"DOI":"10.1016\/s0096-3003(03)00740-9","type":"journal-article","created":{"date-parts":[[2003,12,5]],"date-time":"2003-12-05T06:41:56Z","timestamp":1070606516000},"page":"641-664","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":12,"title":["Some integral and asymptotic formulas associated with the Hurwitz Zeta function"],"prefix":"10.1016","volume":"154","author":[{"given":"S.","family":"Kanemitsu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Kumagai","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.M.","family":"Srivastava","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Yoshimoto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S0096-3003(03)00740-9_BIB1","doi-asserted-by":"crossref","first-page":"1201","DOI":"10.1090\/S0025-5718-99-01051-0","article-title":"Calculation of values of L-functions associated to elliptic curves","volume":"68","author":"Akiyama","year":"1999","journal-title":"Math. Comput."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB2","doi-asserted-by":"crossref","first-page":"161","DOI":"10.2140\/pjm.1951.1.161","article-title":"On the Lerch Zeta function","volume":"1","author":"Apostol","year":"1951","journal-title":"Pacific J. Math."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB3","series-title":"Theory and Application of Special Functions (Proc. Advanced Sem. Math. Res. Center, Univ. Wisconsin, Madison, Wisconsin, 1975)","first-page":"143","article-title":"Periodic Bernoulli numbers, summation formulas and applications","author":"Berndt","year":"1975"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB4","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/0022-314X(75)90045-1","article-title":"Character analogues of the Poisson and Euler\u2013Maclaurin summation formulas with applications","volume":"7","author":"Berndt","year":"1975","journal-title":"J. Number Theory"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB5","series-title":"Ramanujan's Notebooks (Part I)","author":"Berndt","year":"1985"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB6","doi-asserted-by":"crossref","first-page":"23","DOI":"10.4064\/aa-28-1-23-68","article-title":"Periodic analogues of the Euler\u2013Maclaurin and Poisson summation formulas with applications to number theory","volume":"28","author":"Berndt","year":"1975","journal-title":"Acta Arith."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB7","series-title":"Differenzengleichungen und Bestimmte Integrale","author":"B\u00f6hmer","year":"1939"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB8","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1006\/jmaa.1997.5198","article-title":"Sums associated with the Zeta function","volume":"206","author":"Choi","year":"1997","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB9","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1017\/S0004972700014210","article-title":"Some series involving the Zeta function","volume":"51","author":"Choi","year":"1995","journal-title":"Bull. Austral. Math. Soc."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB10","first-page":"171","article-title":"On the analogue of the formula of Chowla and Selberg for real quadratic fields","volume":"351","author":"Deninger","year":"1984","journal-title":"J. Reine Angew. Math."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB11","unstructured":"A. Erd\u00e9lyi, W. Magnus, F. Oberhettinger, F.G. Tricomi (The Bateman Manuscript Project), Higher Transcendental Functions, Vol. I, McGraw-Hill, New York, Toronto, London, 1953"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB12","series-title":"Number Theory and Combinatorics (Japan, 1984)","first-page":"119","article-title":"Fractional part sums and divisor functions","author":"Ishibashi","year":"1985"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB13","first-page":"64","article-title":"On the sum of series that contain values of Riemann and Hurwitz Zeta-functions at lattice points (Russian)","volume":"86","author":"Israilov","year":"1989","journal-title":"Voprosy Vychisl. i Prikl. Mat. (Tashkent)"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB14","first-page":"14","article-title":"Some sums involving Farey fractions","volume":"958","author":"Kanemitsu","year":"1996","journal-title":"RIMS K\u00f4ky\u00fbroku"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/PL00000117","article-title":"On the Hurwitz\u2013Lerch Zeta-function","volume":"59","author":"Kanemitsu","year":"2000","journal-title":"Aequationes Math."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB16","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1011496709753","article-title":"Sums involving the Hurwitz Zeta function","volume":"5","author":"Kanemitsu","year":"2001","journal-title":"Ramanujan J."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB17","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1023\/A:1011449413387","article-title":"On rapidly convergent series expressions for Zeta- and L-values,and log sine integrals","volume":"5","author":"Kanemitsu","year":"2001","journal-title":"Ramanujan J."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB18","doi-asserted-by":"crossref","first-page":"167","DOI":"10.3792\/pjaa.74.167","article-title":"Power series and asymptotic series associated with the Lerch Zeta-function","volume":"74","author":"Katsurada","year":"1998","journal-title":"Proc. Japan Acad. Ser. A Math. Sci."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB19","first-page":"107","article-title":"Rapidly convergent series representations for \u03b6(2n+1) and their \u03c7-analogue","volume":"40","author":"Katsurada","year":"1999","journal-title":"Acta Arith."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB20","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1016\/0022-247X(92)90034-B","article-title":"On the Taylor expansion of the Lerch Zeta-function","volume":"170","author":"Klusch","year":"1992","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB21","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1017\/S0013091500015844","article-title":"Generalized Euler constants","volume":"21","author":"Knopmacher","year":"1978","journal-title":"Proc. Edinburgh Math. Soc. (Ser. 2)"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB22","first-page":"433","article-title":"The functional equation for Dirichlet L-functions and the problem of divisors in arithmetic progressions (Russian)","volume":"30","author":"Lavrik","year":"1966","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB23","first-page":"91","article-title":"An approximate functional equation for the Dirichlet L-function","volume":"18","author":"Lavrik","year":"1968","journal-title":"Trudy Moskov. Mat. Obshch."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB24","first-page":"70","article-title":"The principle of the theory of nonstandard functional equations for Dirichlet functions, consequences and applications of it (Russian)","volume":"132","author":"Lavrik","year":"1973","journal-title":"Trudy Mat. Inst. Steklov."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB25","first-page":"501","article-title":"Functional equations with a parameter for Zeta-functions (Russian)","volume":"54","author":"Lavrik","year":"1990","journal-title":"Izv. Akad. Nauk SSSR Ser. Mat."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB26","doi-asserted-by":"crossref","first-page":"125","DOI":"10.4064\/aa-27-1-125-142","article-title":"Euler constants for arithmetic progressions","volume":"27","author":"Lehmer","year":"1975","journal-title":"Acta Arith."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB27","first-page":"1","article-title":"Die Dirichletschen Reihen, die zahlentheoretischen Funktionen und die unendlichen Produkte von endlichem Geschlecht","volume":"31","author":"Mellin","year":"1902","journal-title":"Acta Soc. Fenn."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB28","doi-asserted-by":"crossref","first-page":"49","DOI":"10.3792\/pjaa.69.49","article-title":"Shifted divisor problem and random divisor problem","volume":"69","author":"Nakajima","year":"1993","journal-title":"Proc. Japan Acad. Ser. A Math. Sci."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB29","series-title":"Elements of Analytic Number Theory","author":"Pan","year":"1991"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB30","series-title":"Topics in Analytic Number Theory","author":"Rademacher","year":"1973"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB31","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1112\/jlms\/s1-9.3.165","article-title":"Notes on Riemann's \u03b6-function","volume":"9","author":"Ramaswami","year":"1934","journal-title":"J. London Math. Soc."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB32","series-title":"Confluent Hypergeometric Functions","author":"Slater","year":"1960"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB33","first-page":"47","article-title":"Some infinite series associated with the Riemann Zeta function","volume":"35","author":"Srivastava","year":"1987","journal-title":"Yokohama Math. J."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB34","first-page":"1","article-title":"A unified presentation of certain classes of series of the Riemann Zeta function","volume":"14","author":"Srivastava","year":"1988","journal-title":"Riv. Mat. Univ. Parma (Ser. 4)"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB35","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/0022-247X(88)90013-3","article-title":"Sums of certain series of the Riemann Zeta function","volume":"134","author":"Srivastava","year":"1988","journal-title":"J. Math. Anal. Appl."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB36","series-title":"Series Associated with the Zeta and Related Functions","author":"Srivastava","year":"2001"},{"issue":"7","key":"10.1016\/S0096-3003(03)00740-9_BIB37","first-page":"17","article-title":"New rapidly convergent series representations for \u03b6(2n+1), L(2n,\u03c7) and L(2n+1,\u03c7)","volume":"4","author":"Srivastava","year":"2000","journal-title":"Math. Sci. Res. Hot-Line"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB38","first-page":"141","article-title":"Sums of the Riemann Zeta function","volume":"42","author":"Suryanarayana","year":"1974","journal-title":"Math. Student"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB39","doi-asserted-by":"crossref","first-page":"181","DOI":"10.4064\/aa-29-2-181-189","article-title":"Some formulas for the Riemann Zeta function at odd integer argument resulting from Fourier expansions of the Epstein Zeta function","volume":"29","author":"Terras","year":"1976","journal-title":"Acta Arith."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB40","series-title":"Quantum Groups: Formalism and Applications","first-page":"115","article-title":"Quantum groups and Zeta-functions","author":"Ueno","year":"1995"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB41","first-page":"140","article-title":"A note on Euler's constant","volume":"29","author":"Verma","year":"1961","journal-title":"Math. Student"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB42","first-page":"181","article-title":"Summation of some series involving Riemann Zeta function","volume":"25","author":"Verma","year":"1983","journal-title":"Indian J. Math."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB43","series-title":"Gitterpunkte in Mehrdimensionalen Kugeln","author":"Walfisz","year":"1957"},{"key":"10.1016\/S0096-3003(03)00740-9_BIB44","first-page":"90","article-title":"A proof of Burnside's formula for log\u0393(x+1) and certain allied properties of Riemann's \u03b6-function","volume":"52","author":"Wilton","year":"1922","journal-title":"Messenger Math."},{"key":"10.1016\/S0096-3003(03)00740-9_BIB45","first-page":"329","article-title":"A note on the coefficients in the expansion of \u03b6(s,x) in powers of s\u22121","volume":"50","author":"Wilton","year":"1927","journal-title":"Quart. J. Pure Appl. Math."}],"container-title":["Applied Mathematics and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300303007409?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0096300303007409?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T16:06:00Z","timestamp":1758816360000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0096300303007409"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,7]]},"references-count":45,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2004,7]]}},"alternative-id":["S0096300303007409"],"URL":"https:\/\/doi.org\/10.1016\/s0096-3003(03)00740-9","relation":{},"ISSN":["0096-3003"],"issn-type":[{"value":"0096-3003","type":"print"}],"subject":[],"published":{"date-parts":[[2004,7]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Some integral and asymptotic formulas associated with the Hurwitz Zeta function","name":"articletitle","label":"Article Title"},{"value":"Applied Mathematics and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/S0096-3003(03)00740-9","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"converted-article","name":"content_type","label":"Content Type"},{"value":"Copyright \u00a9 2003 Elsevier Inc. All rights reserved.","name":"copyright","label":"Copyright"}]}}